It is common knowledge that when a specimen of a piezoelectric material is driven by a cyclic electric field, "resonances" at particular frequencies can occur depending on the geometry of the specimen and its material properties. Because of the existence of "resonances", resonator measurements have been extensively employed in the determination of the elastic, piezoelectric and dielectric properties of these materials, including, of course, poled ferroelectric materials. The conventional method of discerning the onset of "resonances" is to monitor admittance (or impedance), which becomes large (or small) at such instances. The divergence of admittance is equivalent to the divergence of the time rate of change of the electric displacement, so that these resonances may be viewed as electrical resonances. It is generally believed that the mechanical responses of the specimen also diverge during such instances, so that mechanical resonances are said to occur simultaneously with electrical resonances. This belief has been the basis of much theoretical and experimental work for many years.
Heretofore, electromechanical elements of sound transducers and sonars have been operated at electrical resonant frequencies, which results in the generation of a large amount of heat and degrades the performance of such systems. Operation of sound transducers and sonars at lower electrical resonant frequencies by having larger electromechanical elements would increase the range of the waves generated because of less attenuation but the problem of heat generation still exists.